A split air conditioning system is split between an indoor unit and an outdoor unit – hence, the name. A mini-split air conditioning system operates in the same way, except the indoor unit is actually multiple indoor units. These units are installed in the different rooms or zones that they're meant to cool.
Casement windows are windows that are hinged on the side and open outwards with a crank handle. It is for these types of windows that Casement Air Conditioner is intended. Otherwise, it has the same properties as the Window Air Conditioner.
A window air conditioner is a single unit with all of the parts and components contained inside one box or casing. This type of AC is usually mounted or installed in a window and plugs into a traditional electrical outlet. It’s convenient because it can be moved from window to window as needed and operates independently from a home HVAC system.
Through-the-wall air conditioners are designed to install through a wall, instead of through a window. They’re a great option as a primary source of cooling and heating or can be used to supplement central A/C.